What is x-y=5,x^2+y^2=13 ?

The solution to x-y=5,x^2+y^2=13 is

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x-y=5,x^2+y^2=13

x - y = 5, x^{2} + y^{2} = 13

(x = 3, x = 2, y = - 2 y = - 3)

Solution steps

[x - y = 5 x^{2} + y^{2} = 13]

Isolate

x

for

x - y = 5 : x = 5 + y

Plug the solutions

x = 5 + y

into

x^{2} + y^{2} = 13

For

x^{2} + y^{2} = 13

, subsitute

x

with

5 + y : y = - 2, y = - 3

Plug the solutions

y = - 2, y = - 3

into

x - y = 5

For

x - y = 5

, subsitute

y

with

- 2 : x = 3

For

x - y = 5

, subsitute

y

with

- 3 : x = 2

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x - y = 5, x^{2} + y^{2} = 13

are

(x = 3, x = 2, y = - 2 y = - 3)

2 x + y = 5, x^{2} + y^{2} = 3

2 x - y = 3, x^{2} - x y = - 4

x + 3 y^{2} = 5, 3 x - y = 5 y

(a - b) (a + b) = 16, a + b = 8

f (x) = 0, f (x) = x^{3} - 3 x^{2} + 4